 # Exam-Style Questions on Quadratic Equations

## Problems on Quadratic Equations adapted from questions set in previous Mathematics exams.

### 1.

IGCSE Extended

(a) Show that the equation $$\frac{3}{x+1}+\frac{3x-9}{2}=1$$ can be simplified to $$3x^2-8x-5=0$$.

(b) Solve the equation $$3x^2-8x-5=0$$ showing all of your working and giving answers to three significant figures.

(c) The total surface area of a cone with radius $$x$$ and slant height $$8x$$ is equal to the area of a circle with radius r. Show that $$r = 3x$$.

[The curved surface area, $$A$$, of a cone with radius $$r$$ and slant height $$l$$ is $$A=\pi rl$$.]

### 2.

IB Studies A red rug has a width of $$x-3$$ cm and a length of $$4x$$ cm.

(a) Write down an expression for the area, A, in cm2, of the rug.

The area of the rug is 3240 cm2.

(b) Calculate the value of $$x$$.

(c) Hence, write down the value of the length and of the width of the rug in centimetres.

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